Trim the meat of outside fat. Pat meat dry and season with salt and ¼ teaspoon pepper. Heat 2 tablespoons oil in a 5-quart heavy pot over medium-high heat until it shimmers. Brown meat well on both sides and remove to a dish. Add remaining 2 tablespoons oil to pot, then cook onion and celery over medium-high heat for 10 minutes, stirring occasionally. Add garlic and cook, stirring, 10 minutes more, lowering the heat if vegetables begin sticking. The onions should have reduced quite a bit and be very tender.
Add thyme, fennel seed, red pepper flakes and ½ teaspoon black pepper to the pan. Return meat to pot and add stock, bourbon, sorghum and vinegar. Reduce heat to low and simmer, covered, until meat is very tender, 3 to 3½ hours (you can also transfer meat to a slow cooker and cook on low heat for 8 hours or more).
Remove meat from sauce and discard bones and any obvious fat. Cover and chill meat and sauce separately. To serve, discard any fat from the top of the sauce and reheat meat and sauce together until warm through (on top of the stove or in a 350° oven, covered, for 30 minutes or so).
Serves 6. Serve with dumpling-style noodles, grits, potatoes, or over rice.